We want every learner in our care to be able to say

**I can attend to precision.**

CCSS.MATH.PRACTICE.MP6

But what if I can’t attend to precision yet? What if I need help? How might we make a pathway for success?

** **

Level 4:

I can distinguish between necessary and sufficient conditions for definitions, conjectures, and conclusions.

Level 3:

I can attend to precision.

Level 2:

I can communicate my reasoning using proper mathematical vocabulary and symbols, and I can express my solution with units.

Level 1:

I can write in complete mathematical sentences using equality and inequality signs appropriately and consistently.

** **

How many times have you seen a misused equals sign? Or mathematical statements that are fragments?

A student was writing the equation of a tangent line to linearize a curve at the point (2,-4).

He had written

y+4=3(x-2)

And then he wrote:

He absolutely knows what he means: y=-4+3(x-2).

But that’s not what he wrote.

** **

Which student responses show attention to precision for the domain and range of y=(x-3)2+4? Are there others that you and your students would accept?

How often do our students notice that we model **attend to precision**? How often to our students notice when we don’t model **attend to precision**?

**Attend to precision** isn’t just about numerical precision. **Attend to precision** is also about the language that we use to communicate mathematically: the distance between a point and a line isn’t just “straight” – it’s the length of the segment that is perpendicular from the point to the line. (How many times have you told your Euclidean geometry students “all lines are straight”?)

But it’s also about learning to communicate mathematically together – and not just expecting students to read and record the correct vocabulary from a textbook.

[Cross posted on Experiments in Learning by Doing]

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howardat58

April 9, 2015 at 5:05 pm

There is a fine line between being precise and being pedantic !!

I got this from the CCSSM document:

“Understand that a function from one set (called the domain) to

another set (called the range) assigns to each element of the domain

exactly one element of the range. If f is a function and x is an element

of its domain, then f(x) denotes the output of f corresponding to the

input x. The graph of f is the graph of the equation y = f(x).”

There was another bit about the domain, which is mathematically correct as well.

So, the domain is any subset of the set (of numbers in this case) for which the function can generate an output, and the range is any set which includes all the outputs for the given domain.

Thus some more of the many alternatives given by the students are technically correct.

I have written lots of stuff on this precision thing. there is no benefit to using fancy jargon if it is not used correctly There are some horrors in the CCSSM document. “Add 3+5+8” for example. Quite common is “Subtract a and b”.

Sometimes writing on lined paper might be of help to the students. (I do sound so old fashioned sometimes). The only thing I see wrong about the 10/2x=10 problem is the solitary divide by 10.

PS I think you are doing an amazing job, and I love reading your posts!

jwilson828

April 10, 2015 at 8:52 am

Thank you, Howard. I appreciate your careful and thoughtful reading. Your questions and comments make me think and learn.

Trisha Gilbreath

April 9, 2015 at 6:24 pm

When asking for the domain of a function, is it understood that one is asking for the entire domain?

It is sometimes difficult to be precise in mathematics because of the variations in definitions. For most of us, domain is defined as the entire set of values for the which the function can generate an output. But, if you can probably find two books in your classroom right now with slightly different definitions. I’ve run into this problem with everything from the definition of rational functions to the idea of increasing, decreasing, and constant portions of a function. However, I think the conversation is more important that the outcome. For example, during class I will not immediately give credit to students who give imprecise answers. Afterwards, we discuss the variations, agree on a standard, and often take a vote on whether or not the answers that show understanding, but lack precision, are given credit.